Comment Re:Not yet? Really? (Score 5, Informative) 910
Well this comment shows the problem right away. This is actually a mass independent problem, as gravity is always accelerating things (on Earth) at ~9.81 m/s^2. The problem is more what the drag on the bus is over the course of the flight. However, since I am not in the mood to calculate Reynolds numbers for flying busses, I will assume inviscid air.
Problem statement: A point particle moving at 70 MPH at some angle must cross a 50 foot gap, and be at the same height when it reaches the other side.
Given:
v0 = 70 mph // Initial speed
x = 50 feet // Distance to travel horizontially
Assumption: Force-free motion
Constant gravity ( g = 9.81 m/s^2 )
Solution:
v0 = 70 mph = 31.2928 m/s
x = 50 feet = 15.24 m
t = Time of flight
theta = Angle from horizon
x = v0*t*cos(theta)
y = v0*sin(theta)*t - g*t^2
Solve for t t = x/(v0*cos(theta))
Substitude into y equation
y = x*v0/v0*sin(theta)/cos(theta) - g*x^2/v0^2/cos(theta)^2
Set y = 0 and solve
x*sin(theta)/cos(theta) = g*x^2/v0^2/cos(theta)^2
sin(theta)*cos(theta) = g*x/v0^2
g*x/v0^2 = 9.81*15.24/(31.2928)^2 = 0.15267
sin(theta)*cos(theta) = 0.15267 can be solve graphically. The first valid solution is 8.89 degrees.
So yes, a bus (with no friction) can cross a 50 feet gap, if the ramp was at an incline greater than 8.89 degrees.
Yay.
Problem statement: A point particle moving at 70 MPH at some angle must cross a 50 foot gap, and be at the same height when it reaches the other side.
Given:
v0 = 70 mph
x = 50 feet
Assumption: Force-free motion
Constant gravity ( g = 9.81 m/s^2 )
Solution:
v0 = 70 mph = 31.2928 m/s
x = 50 feet = 15.24 m
t = Time of flight
theta = Angle from horizon
x = v0*t*cos(theta)
y = v0*sin(theta)*t - g*t^2
Solve for t t = x/(v0*cos(theta))
Substitude into y equation
y = x*v0/v0*sin(theta)/cos(theta) - g*x^2/v0^2/cos(theta)^2
Set y = 0 and solve
x*sin(theta)/cos(theta) = g*x^2/v0^2/cos(theta)^2
sin(theta)*cos(theta) = g*x/v0^2
g*x/v0^2 = 9.81*15.24/(31.2928)^2 = 0.15267
sin(theta)*cos(theta) = 0.15267 can be solve graphically. The first valid solution is 8.89 degrees.
So yes, a bus (with no friction) can cross a 50 feet gap, if the ramp was at an incline greater than 8.89 degrees.
Yay.